chance of 2 campers having the same schedule assuming that all schedules are unique but 10% of campers incorrectly follow their schedule

nodeCampAttack.js

//git clone https://gist.github.com/5914750.git
//node 5914750/nodeCampAttack

var classes = 8;
var schedules = 1; for(var i = 2; i <= classes; i++) schedules *= i; //8!
var mistakeRate = 0.1; //10% chance that a participant doesn't follow their schedule
var hitChance = 0.5; //what we're solving for

var missChance = 1; //100% (can't collide without participants)
var participant = 1;
while(missChance > 1 - hitChance) {
    var usedSchedules = participant - 1;
    var errorSchedules = usedSchedules * mistakeRate;

    var notUsed = (schedules - usedSchedules) / schedules; //chance of selecting a schedule at random that's unused
    var notMistaken = (schedules - errorSchedules) / schedules; //chance of selecting a schedule that's not used by a mistaken participant

    var collisionChance = 0;
    collisionChance += mistakeRate * notUsed; //if this participant is mistaken they can collide with anyone
    collisionChance += (1 - mistakeRate) * notMistaken; //if this participant isn't mistaken they can only collide with mistaken participants

    missChance *= collisionChance; //chance of missing up to this one is the chance of missing up to the last one times the chance of missing this one
    console.log(participant + " " + (1 - missChance) * 100);
    participant++;
}